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A208598 Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero. 2
6, 23, 60, 125, 226, 371, 568, 825, 1150, 1551, 2036, 2613, 3290, 4075, 4976, 6001, 7158, 8455, 9900, 11501, 13266, 15203, 17320, 19625, 22126, 24831, 27748, 30885, 34250, 37851, 41696, 45793, 50150, 54775, 59676, 64861, 70338, 76115, 82200, 88601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 4 of A208597.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = (4/3)*n^3 + 2*n^2 + (5/3)*n + 1.

Conjectures from Colin Barker, Mar 07 2018: (Start)

G.f.: x*(6 - x + 4*x^2 - x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

EXAMPLE

Some solutions for n=4:

  -3  -4  -3  -3  -4  -2  -2  -3  -4  -2  -3  -1  -4  -3  -4  -4

   1  -2   4   3   0   0   0  -1   1  -2   4  -1   2  -1   1  -1

   4   2   0  -3   3  -2   0   3   1   4  -1   2  -2   4   0   3

  -2   4  -1   3   1   4   2   1   2   0   0   0   4   0   3   2

CROSSREFS

Cf. A208597.

Sequence in context: A273214 A273276 A273252 * A119712 A273314 A281424

Adjacent sequences:  A208595 A208596 A208597 * A208599 A208600 A208601

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 29 2012

STATUS

approved

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Last modified October 18 23:07 EDT 2018. Contains 316327 sequences. (Running on oeis4.)